HOW THE BRAIN WORKS, MAYBE

By TIMOTHY FERRIS; Timothy Ferris, a professor in the Graduate School of Journalism at the University of California, Berkeley, is the author of ''Coming of Age in the Milky Way.''

Published: November 19, 1989

THE EMPEROR'S NEW MIND Concerning Computers, Minds, and the Laws of Physics. By Roger Penrose. Illustrated. 466 pp. New York: Oxford University Press. $24.95.

Given that hubris stalks heroes, it is not surprising that today's scientists, with so many heroic accomplishments behind them, sometimes expect more from their brightest new ideas than they can deliver. This may explain why the rosiest forecasts of imminent triumph are being heard these days from researchers in two fields - theoretical physics and computer science - most flush with the glow of recent success.

The theoretical physicists, having mastered an enormous range of natural phenomena from black holes to nuclear bombs, are talking about developing a so-called superunified theory or theory of everything (T.O.E.), a masterful set of equations that would embrace both quantum mechanics and relativity, the two grand pillars of modern physics. A T.O.E. would bring new depths of understanding to every basic process in nature, from the death of stars to the birth of the universe. It would, however, be a reductionist theory, concerned principally with simple interactions and far removed from such complicated phenomena as life and thought. And yet we find similar optimism at the complex end of the spectrum, too. Many mathematicians working in computer science propose that it will soon be possible to build computers capable of artificial intelligence, machines that could equal or excel the thought processes of the human mind.

Roger Penrose, who teaches mathematics at the University of Oxford, begs to differ. He thinks that what goes on in the human mind - and in the minds of apes and dolphins, for that matter - is very different from the workings of any existing or imaginable computer. In ''The Emperor's New Mind,'' a bold, brilliant, groundbreaking work, he argues that we lack a fundamentally important insight into physics, without which we will never be able to comprehend the mind. Moreover, he suggests, this insight may be the same one that will be required before we can write a unified theory of everything.

This is an astonishing claim, one that the critical reader might be tempted to dismiss out of hand were it broached by a thinker of lesser stature. But Mr. Penrose is a gifted mathematician with an impressive record of lighting lamps that have helped guide physics on its way. His research with Stephen Hawking aided in establishing the plausibility of black holes, and brought new insights into the physics of the big bang with which the expansion of the universe is thought to have begun. His work in the early 1970's, on the geometry of what are called aperiodic tiles, impressive just as a matter of pure mathematical invention, turned out to describe the architecture of a new class of crystals the existence of which was not yet known at the time. So when Mr. Penrose talks, scientists listen.

In his new book, Mr. Penrose attempts to sketch the outlines of a future theory that would link relativity, quantum physics and the phenomenon of intelligence. As he does not know precisely what such a theory would say, he is obliged to tread often on the thin ice of speculation. ''I am putting my neck out here,'' he confesses at one point, and his paragraphs bristle with qualifying terms like ''suggest,'' ''perhaps'' and ''maybe.'' Indeed, much of the charm of the book resides in his cheerful willingness to hold his considerable reputation hostage to so unlikely a crusade.

This is not to say that ''The Emperor's New Mind'' is woolly-minded in the slightest. It is just about as rigorous as it could be, so much so that readers lacking at least a graduate student's comprehension of physics will find parts of it rough going. Yet it is also as clear as it could be; Mr. Penrose has obviously taken pains to make his book accessible without compromising his subject matter, and he interrupts himself periodically to urge his readers on. (''I have tried not to cheat, and we shall have to work a little harder,'' he warns, at the start of his explication of quantum mechanics.) At 466 pages, the book is also about as short as it could be; scarcely a word is wasted, and even the digressions, which Mr. Penrose is careful to label as such, are generally too interesting to skip. All of which is to say that Mr. Penrose's case is too far-reaching and subtle to be translated accurately into a brief summary. I will now attempt such a summary, but it is no substitute for the book.

The proponents of the ''strong A.I.'' strain of artificial intelligence argue that the brain is a computer. Mr. Penrose responds that computers have inherent limits, which, while clearly acknowledged in the foundations of computation theory, are not necessarily imposed on human thought.

One such limitation derives from the fact that all computers are ''Turing machines.'' As the British mathematician Alan Turing (1912-54) established, such a machine (which is, of course, a mathematical concept and only secondarily a particular piece of hardware) can deal only with what are called computable numbers. Yet there is a rich and useful branch of mathematics that traffics in noncomputable numbers. Indeed, as Mr. Penrose demonstrates, even many of the ordinary processes addressed by Newtonian mechanics are noncomputable: it is, for instance, possible to predict the outcome of a billiard shot using Newton's equations, but a strong break in a game of eight-ball begins to tax the system, and the collisions experienced by the molecules of air in a thimble in one millisecond quite overwhelm it. If mathematicians are only computers, Mr. Penrose asks, how are they capable of achieving useful insights in fields of thought - such as noncomputable numbers - that ought in principle to be inaccessible to computers?